Problem: The arithmetic sequence $(a_i)$ is defined by the formula: $a_1 = -9$ $a_i = a_{i-1} - 3$ What is $a_{9}$, the ninth term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $-9$ and the common difference is $-3$ To find the ninth term, we can rewrite the given recurrence as an explicit formula. The general form for an arithmetic sequence is $a_i = a_1 + d(i - 1)$ . In this case, we have $a_i = -9 - 3(i - 1)$ To find $a_{9}$ , we can simply substitute $i = 9$ into the our formula. Therefore, the ninth term is equal to $a_{9} = -9 - 3 (9 - 1) = -33$.